What are the divisors of 5086?

1, 2, 2543, 5086

2 even divisors

2, 5086

2 odd divisors

1, 2543

How to compute the divisors of 5086?

A number N is said to be divisible by a number M (with M non-zero) if, when we divide N by M, the remainder of the division is zero.

N mod M = 0

Brute force algorithm

We could start by using a brute-force method which would involve dividing 5086 by each of the numbers from 1 to 5086 to determine which ones have a remainder equal to 0.

Remainder = N ( M × N M )

(where N M is the integer part of the quotient)

  • 5086 / 1 = 5086 (the remainder is 0, so 1 is a divisor of 5086)
  • 5086 / 2 = 2543 (the remainder is 0, so 2 is a divisor of 5086)
  • 5086 / 3 = 1695.3333333333 (the remainder is 1, so 3 is not a divisor of 5086)
  • ...
  • 5086 / 5085 = 1.0001966568338 (the remainder is 1, so 5085 is not a divisor of 5086)
  • 5086 / 5086 = 1 (the remainder is 0, so 5086 is a divisor of 5086)

Improved algorithm using square-root

However, there is another slightly better approach that reduces the number of iterations by testing only integers less than or equal to the square root of 5086 (i.e. 71.316197318702). Indeed, if a number N has a divisor D greater than its square root, then there is necessarily a smaller divisor d such that:

D × d = N

(thus, if N D = d , then N d = D )

  • 5086 / 1 = 5086 (the remainder is 0, so 1 and 5086 are divisors of 5086)
  • 5086 / 2 = 2543 (the remainder is 0, so 2 and 2543 are divisors of 5086)
  • 5086 / 3 = 1695.3333333333 (the remainder is 1, so 3 is not a divisor of 5086)
  • ...
  • 5086 / 70 = 72.657142857143 (the remainder is 46, so 70 is not a divisor of 5086)
  • 5086 / 71 = 71.633802816901 (the remainder is 45, so 71 is not a divisor of 5086)